Investigation and Development of Algorithms And Techniques for Microwave Tomography

This thesis reports on research undertaken in the area of microwave tomography (MWT) where the goal is to find the dielectric profile of an object of interest using microwave measurements collected outside the object. The main focus of this research is on the development of inversion algorithms which solve the electromagnetic inverse scattering problem associated with MWT. These algorithms must deal with two different aspects of the inverse problem: its nonlinearity and ill-posedness. After providing an overview of some of the different possible formulations in terms of a nonlinear optimization problem, details on the use of the Gauss-Newton inversion algorithm which solves this problem are given. Various regularization techniques for the Gauss-Newton inversion algorithm are studied and classified. It is shown that these regularization techniques can be viewed from within a single consistent framework after applying some modifications. Within the framework of the two-dimensional MWT problem, the inversion of transverse magnetic and transverse electric data sets are considered and compared in terms of computational complexity, image quality and convergence rate.;The MWT problem is also formulated for MWT chambers made of conducting cylinders of arbitrary shapes. A Gauss-Newton inversion algorithm is utilized to invert the data collected in such configurations. It is then shown that collecting microwave scattered-field data inside MWT setups with different boundary conditions can provide a robust set of useful information for the reconstruction of the dielectric profile. To produce good quality reconstructions, the amount of data collected under each boundary condition can be relatively small if the number of different boundary condition configurations is sufficiently high. This leads to a novel MWT setup wherein a rotatable conductive triangular enclosure is used to generate scattered-field data. Antenna arrays, with as few as only four elements, that are fixed with respect to the object of interest can provide sufficient data to give good reconstructions, if the triangular enclosure is rotated a sufficient number of times.;Preliminary results of using the algorithms presented herein on data collected using two different MWT prototypes currently under development by the University of Manitoba's Electromagnetic Imaging Group are reported. Using the current open-region MWT prototype, an experimental resolution study using the Gauss-Newton inversion method was performed using various cylindrical targets. Results of this resolution study are reported herein and the separation resolution limit of this system is quantified.;A new solution to the contrast source inversion formulation of the microwave tomography problem for the case where the MWT chamber consists of a circular conductive enclosure is introduced. This solution is based on expressing the unknowns of the problem as truncated eigenfunction expansions corresponding to the Helmholtz operator for a homogeneous background medium with appropriate boundary conditions imposed at the chamber walls.